Academic Standards

KY.HS.G.1: Know and apply precise definitions of the language of Geometry:

Circles

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Inscribed Angles

Parallel, Intersecting, and Skew Lines

KY.HS.G.1.a: Understand properties of line segments, angles and circle.

Chords and Arcs

Circles

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Inscribed Angles

Investigating Angle Theorems

Parallel, Intersecting, and Skew Lines

Segment and Angle Bisectors

KY.HS.G.1.b: Understand properties of and differences between perpendicular and parallel lines.

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Parallel, Intersecting, and Skew Lines

KY.HS.G.2: Representing transformations in the plane.

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

KY.HS.G.2.a: Describe transformations as functions that take points in the plane as inputs and give other points as outputs.

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

KY.HS.G.2.b: Compare transformations that preserve distance and angle measures to those that do not.

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

KY.HS.G.2.c: Given a rectangle, parallelogram, trapezoid, or regular polygon, formally describe the rotations and reflections that carry it onto itself, using properties of these figures.

Reflections

Rotations, Reflections, and Translations

Similar Figures

KY.HS.G.3: Develop formal definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

Circles

Dilations

Reflections

Rotations, Reflections, and Translations

Similar Figures

Translations

KY.HS.G.4: Understand the effects of transformations of geometric figures.

KY.HS.G.4.a: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure.

Dilations

Reflections

Rotations, Reflections, and Translations

Similar Figures

Translations

KY.HS.G.4.b: Specify a sequence of transformations that will carry a given figure onto another.

Dilations

Reflections

Rotations, Reflections, and Translations

Similar Figures

Translations

KY.HS.G.4.c: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Absolute Value with Linear Functions

Circles

Dilations

Holiday Snowflake Designer

Reflections

Rotations, Reflections, and Translations

Similar Figures

Translations

KY.HS.G.5: Know and apply the concepts of triangle congruence:

KY.HS.G.5.a: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

KY.HS.G.5.b: Explain how the criteria for triangle congruence (ASA, SAS and SSS) follow from the definition of congruence in terms of rigid motions.

KY.HS.G.6: Apply theorems for lines, angles, triangles, parallelograms.

Constructing Parallel and Perpendicular Lines

Investigating Angle Theorems

Isosceles and Equilateral Triangles

Parallelogram Conditions

Polygon Angle Sum

Special Parallelograms

Triangle Angle Sum

Triangle Inequalities

KY.HS.G.7: Prove theorems about geometric figures.

KY.HS.G.7.a: Construct formal proofs to justify theorems for lines, angles and triangles.

Congruence in Right Triangles

Investigating Angle Theorems

Isosceles and Equilateral Triangles

Triangle Angle Sum

Triangle Inequalities

KY.HS.G.7.b: Construct formal proofs to justify theorems for parallelograms.

Parallelogram Conditions

Special Parallelograms

KY.HS.G.8: Create and apply geometric constructions.

KY.HS.G.8.a: Make formal geometric constructions with a variety of tools and methods.

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Segment and Angle Bisectors

KY.HS.G.8.b: Apply basic construction procedures to construct more complex figures.

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Segment and Angle Bisectors

KY.HS.G.9: Understand properties of dilations.

KY.HS.G.9.a: Verify the properties that result from that dilations given by a center and a scale factor.

KY.HS.G.9.b: Verify that a dilation produces an image that is similar to the pre-image.

Circles

Dilations

Similar Figures

KY.HS.G.10: Apply the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Proving Triangles Congruent

Similar Figures

KY.HS.G.11: Understand theorems about triangles.

KY.HS.G.11.a: Apply theorems about triangles.

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Similar Figures

Similarity in Right Triangles

KY.HS.G.11.b: Prove theorems about triangles.

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Similar Figures

Similarity in Right Triangles

KY.HS.G.11.c: Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Chords and Arcs

Congruence in Right Triangles

Constructing Congruent Segments and Angles

Dilations

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures

Similarity in Right Triangles

KY.HS.G.12: Understand properties of right triangles.

KY.HS.G.12.a: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles (sine, cosine and tangent).

Sine, Cosine, and Tangent Ratios

KY.HS.G.12.b: Explain and use the relationship between the sine and cosine of complementary angles.

KY.HS.G.12.c: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Cosine Function

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

KY.HS.G.15: Verify using dilations that all circles are similar.

KY.HS.G.16: Identify and describe relationships among angles and segments within the context of circles involving:

KY.HS.G.16.a: Recognize differences between and properties of inscribed, central and circumscribed angles.

Chords and Arcs

Inscribed Angles

KY.HS.G.16.b: Understand relationships between inscribed angles and the diameter of a circle.

Circumference and Area of Circles

Inscribed Angles

KY.HS.G.17: Apply basic construction procedures within the context of a circle.

KY.HS.G.17.a: Construct the inscribed and circumscribed circles of a triangle.

Concurrent Lines, Medians, and Altitudes

KY.HS.G.18: Understand the relationship between an intercepted arc length within a circle and the radius of the circle.

KY.HS.G.18.a: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius. Derive the formula for the area of a sector.

KY.HS.G.18.b: Define the radian measure of the angle as the measure of a central angle that intercepts an arc equal in length to the radius of the circle.

Cosine Function

Sine Function

Tangent Function

KY.HS.G.19: Understand the relationship between the algebraic form and the geometric representation of a circle.

KY.HS.G.19.a: Write the equation of a circle of given center and radius using the Pythagorean Theorem.

KY.HS.G.19.b: Derive and write the equation of a circle of given center and radius using the Pythagorean Theorem.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

KY.HS.G.19.c: Complete the square to find the center and radius of a circle given by an equation.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

KY.HS.G.20: Derive the equations of conic sections.

KY.HS.G.20.a: Derive the equation of a parabola given a focus and directrix.

KY.HS.G.20.b: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

KY.HS.G.22: Justify and apply the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

KY.HS.G.23: Find measurements among points within the coordinate plane.

KY.HS.G.23.a: Use points from the coordinate plane to find the coordinates of a midpoint of a line segment and the distance between the endpoints of a line segment.

KY.HS.G.24: Use coordinates within the coordinate plane to calculate measurements of two dimensional figures.

KY.HS.G.24.a: Compute the perimeters of various polygons.

KY.HS.G.24.b: Compute the areas of triangles, rectangles and other quadrilaterals.

KY.HS.G.25: Analyze and determine the validity of arguments for the formulas for the various figures and shapes.

Circumference and Area of Circles

Prisms and Cylinders

Pyramids and Cones

KY.HS.G.25.a: Finding the circumference and area of a circle.

Circumference and Area of Circles

Prisms and Cylinders

Pyramids and Cones

KY.HS.G.25.b: Finding the volume of a sphere, prism, cylinder, pyramid and cone.

Prisms and Cylinders

Pyramids and Cones

KY.HS.G.26: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Prisms and Cylinders

Pyramids and Cones

KY.HS.G.27: Use volume formulas to solve problems for cylinders, pyramids, cones, spheres, prisms.

Prisms and Cylinders

Pyramids and Cones

KY.HS.G.28: Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.

KY.HS.G.29: Use geometric shapes, their measures and their properties to describe objects in real world settings.

Prisms and Cylinders

Pyramids and Cones

KY.HS.G.30: Apply concepts of density based on area and volume in modeling situations, using appropriate units of measurement.

Correlation last revised: 9/15/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.